Given

• Magnetic flux: $\phi(t)=5t^2-36t+1$
• Resistance of circuit: $R=8\,\Omega$
• Time: $t=2\,\text{s}$

Use Faraday’s law The induced emf is $e=-\frac{d\phi}{dt}$

Differentiate the flux $\frac{d\phi}{dt}=\frac{d}{dt}(5t^2-36t+1)=10t-36$

Find emf at $t=2$ s $e=-(10\cdot 2-36)=-(20-36)=16\,\text{V}$

So the magnitude of induced emf is $|e|=16\,\text{V}$

Find induced current using Ohm’s law $I=\frac{|e|}{R}=\frac{16}{8}=2\,\text{A}$

Final answer The induced current at $t=2\,$s is $\boxed{2\,\text{A}}$